B(C) MESON PRODUCTIONS VIA INDUCED GLUON FRAGMENTATION

Gluons cannot directly fragment into B(c) mesons until at order alpha( s)3. However, the Altarelli-Parisi evolution of the bBAR-quark fragmen tation functions D(b-->Bc) (z) and D(b-->Bc) (z) from the heavy quark mass scales up to the collider energy scale Q can induce the gluon fr agmentation functions D(g-->Bc) (z) and D(g-->Bc) (z), respectively, at the order alpha(s)3 log (Q/m(b,c)) through the gluon splitting g--> b. We will determine these induced gluon fragmentation functions. The B(c) meson productions due to the induced gluon fragmentation will be evaluated and compared to the productions by the direct bBAR-quark fra gmentation. The contribution from the induced gluon fragmentation is f ound to be a fairly large portion of the total B(c) and B(c) meson pr oductions, and therefore cannot be ignored